Topology in 2D non-Abelian Lattice Gauge Theories

Abstract

In two dimensions, $U(N_c)$ gauge theories exhibit a non-trivial topological structure, while $SU(N_c)$ theories are topologically trivial. Hence, for $G=U(N_c)$ the phase space is divided into topological sectors, characterized by a topological index (a.k.a. ``topological charge''). These sectors are separated by action barriers, which diverge if the lattice spacing is taken small, resulting in an algorithmic problem known as ``topological freezing''. We study these theories in various box sizes and at various couplings. With the help of gradient flow we derive instanton-like solutions for 2D $U(N_c)$ theory with a specific focus on the case of $N_c=2$.

Comments: 8 pages, 7 figures, 1 table. Proceedings of the 41st International Symposium on Lattice Field Theory (LATTICE2024), 28 July - 3 August, 2024 Liverpool, UK